Nonlinear oscillation of first order delay differential equations
type: Item
instance of: scholarly article
title: Nonlinear oscillation of first order delay differential equations
zbMATH Open document ID: 0852.34064
author: Norio Yoshida
published in: Rocky Mountain Journal of Mathematics
publication date: 1996-08-05T00:00:00Z
full work available at URL: contents.htm
review text: In the first section of the paper, the author considers the nonlinear delay differential equation (1) \(y'(t)+ p(t) f(y(\sigma(t)))= q(t)\) under the following hypotheses: \(p(t)\in C([t_0, \infty); [0, \infty))\), \(q(t)\in C([t_0, \infty); \mathbb{R}^1)\); \(f(s)\in C(\mathbb{R}^1; \mathbb{R}^1)\), \(f(s)\geq 0\), for \(s\geq 0\), \(f(- s)= - f(s)\) for \(s> 0\), and \(f(s)\) is nondecreasing for \(s\geq 0\); \(\sigma(t)\in C([t_0, \infty); \mathbb{R}^1)\), \(\lim_{t\to \infty}\sigma(t)= \infty\), \(\sigma(t)\leq t\) for \(t\geq t_0\), and \(\sigma(s)\) is nondecreasing for \(s\geq 0\). Sufficient conditions are obtained under which all solutions of (1) are oscillatory. In the second section the more general equation \[ y'(t)+ a(t) y(t)+ \sum^k_{i= 1} b_i(t) y(\rho_i(t))+ p(t) f(y(\sigma(t)))= q(t)\tag{2} \] is considered. Applying the results on equation (1), oscillation criteria for equation (2) are established. Examples are also given that illustrate the main results of the author.
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 894690
zbMATH Keywords: nonlinear delay differential equation
zbMATH Keywords: oscillation criteria
reviewed by: V. Petrov
MaRDI profile type: Publication
OpenAlex ID: W2071237377
cites work: Q4001772
cites work: Q4007285
cites work: Q4000352
cites work: Q3759218
cites work: Q4186655
cites work: Q4893323
cites work: Oscillatory behaviour of an equation arising from an industrial problem
DOI: 10.1216/RMJM/1181072122
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description: scientific article; zbMATH DE number 894690